If . . . then? An Introduction to Logic.

Part 1. Section 4b

Slippery slope fallacy

To introduce our next fallacy, recall the valid argument form hypothetical syllogism /chain of reasoning from Section 3:

If p then q

If q then r

Therefore if p then r

As it turns out we could easily add more 'links' in the chain of reasoning like this:

If p then q

If q then r

If r then s

If s then m

⋮

If y then z

Therefore if p then z

The above extended version of the chain of reasoning is still a valid form, which means that for any substitution of the variables p through z which results in all true premises (links in the chain), then the conclusion must be true.

The fallacy known as the slippery slope is similar to the chain in reasoning with the exception that each 'if . . .then' link in the chain is connected, not by the necessity of implication, but only in the form of weak possibility, hence we have:

If p then possiblyq

If q then possiblyr

Therefore if p then most likelyr

In the case of the slippery slope fallacy, the 'possibly' part is usually suppressed and the 'most likely' part is many times emphasized in some way. Here are some examples:

If we legalize marijuana for medicinal purposes, then we will soon legalize it for recreational purposes, which means we will soon be legalizing heroine.

If we allow you to go on your first date before you are 16, then we will end up allowing your sister to go on a date before she is 15 and finally your little sister will end up going on a date before she is 14 and getting married by the time she is 15.

Slippery slope

Definition: When an inference is made from a chain of reasoning where each link in the chain represents only a possible, rather than a probable outcome, the resulting error in reasoning is known as the slippery slope fallacy.

Strawman fallacy

The next fallacy we introduce is perhaps one of the most common fallacies encountered in the world of arguments and counter-arguments, and one of the most difficult fallacies to detect. The fallacy is known as the strawman fallacy, and just as the name suggests, the fallacy attacks a weaker version of an argument (the strawman) rather than the actual argument itself. It is difficult to detect since one must know the details of the actual argument before one can detect that the version being attacked is a strawman version. Here are two classic examples:

Evolution can't be a correct theory since it postulates that humans evolved from monkeys. But monkeys still exist today, so the theory of evolution must be wrong.

Dover City Colorado just experienced its coldest week in the history of record keeping, which goes back over 100 years. Hence global warming is false, as it states that global temperatures have been increasing for several years and will continue to increase.

The first is an example of a straw man argument since it mischaracterizes the theory of evolution which postulates that humans and monkeys (and indeed all mammals) descended from a common ancestor or ancestors millions of years ago. The second argument mischaracterizes the claims of global warming which state average global temperatures have been rising for several years and will continue to rise for the foreseeable future unless great efforts are made to reduce green-house gases.

Strawman fallacy

Definition: When an inference is made from a position or argument which has been mischaracterized in such a way as to make it easier to argue against, the resulting error in reasoning is known as the straw man fallacy.

Begging the question and the complex question

Our last two fallacies are errors in reasoning of a different type. The previous errors in reasoning can be classified as weak arguments in the classification scheme of Section 1 Part 2, with the additional property of being common and perhaps psychologically persuasive for one reason or the other. This is not the case for the fallacies known as begging the question and complex question, which commit an error of reasoning by assuming the very thing they should argue for or prove - hence technically these arguments are valid, but the error in reasoning is that the premises are the same as the conclusion.

Before we provide some examples, let's examine this symbolically. As always, where p, q, r, etc. are statement variables, convince yourself that both of the following argument forms are valid:

Form 1.

p

Therefore p

Form 2.

p

q

r

s

Therefore p

Notice that in both Form 1 and Form 2 the conclusion p is actually one of the premises, which makes it impossible to have all tue premises and a false conclusion, so the inference is valid - why then is it an error in reasoning? This question is important enough that you should think about it for a second or two and check your thoughts by answering the following question:

Value: 5

Form 1 and Form 2 are errors in reasoning because . . . ?

a. The forms look more like invalid forms than valid forms, which may lead one to confuse an invalid inference for a valid inference.

b. The forms are valid, but they can never be sound.

c. Errors in reasoning are usually weak arguments, and hence do not have valid inferences. These examples do have valid inferences, so the error in reasoning is to confuse them with other more common types of fallacies.

d. If they were not errors in reasoning, they could be used to prove anything, since the variable p can stand for any proposition, including absurd ones (let p be, 'the moon is made of green cheese' for example). Additionally, the entire point of an argument is to give reasons why a claim is true based on other reasons. These arguments assume the very thing they are supposed to prove.

When an argument assumes the very thing it is suppose to prove, then the resulting fallacy is known as begging the question, also known as circular reasoning or petitio principii. Here is an example:

Mystic: I use a Ouija board to gain insights into people's futures and their personality.

Skeptic: But how do you know that the Ouija board reports the truth?

Mystic: The Ouija board says so itself, it once spelled out :

W H A T I S C L A I M E D H E R E I S T R U E

Notice that the point to be proven is that the Ouija board reports the truth. The Mystic assumes it does and gives that as a reason supporting the truth of the claim that the Ouija board tells the truth.

A closely related fallacy is called the fallacy of the complex question, where a question is asked in such a way that it assumes the truth of the very thing it is supposed to illicit by way of an answer. Here is an example:

When was the last time you drove intoxicated?

In this case the question presupposes that the person has in the past driven intoxicated, which supposedly is the point of asking the question in the first place - specifically to find out whether a person have ever driven intoxicated or not.

Begging the question and complex question

Definition: When an argument assumes, explicitly or implicitly, the very thing it is supposed to conclude, the resulting error in reasoning is known as begging the question. If a question is asked in such a way as to presuppose an answer, the resulting error in reasoning is called the fallacy of the complex question.

Test your ability to recognize the fallacies covered in Section 4.4 by taking the following quiz: